| fs = abs-files(files), ofh = abs-of(of), path = q + str ', root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced, ⌊err1⌋ ∨ err1 = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err1 = EACCESS ∧ p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ ⟨choose err with pre-mkdir(path, md, err, user, root, fs, ofh) in err0 := err; if err0 = ESUCCESS then root[path] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0), err1 = ESUCCESS |
fs = abs-files(files), ofh = abs-of(of), path = q + str ', root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced, ⌊err1⌋ ∨ err1 = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err1 = EACCESS ∧ p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ ∃ err. pre-mkdir(path, md, err, user, root, fs, ofh) ∧ ⟨err0 := err; if err0 = ESUCCESS then root[path] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0), err1 = ESUCCESS